The algorithm exploits the following property of exponential random variables: for each \(1 \le j \le r\)  the random variable \(\tilde{W_{j}} = \min _{1 \le i \le k}{W_{j}^{i}}\)  is distributed exponentially with mean \(1/\tilde{y}\)  where \(\tilde{y} = \sum _{i=1}^{k}{y_{i}}\) . Therefore, the quantity we want to estimate is the reciprocal of the expectation of \(\tilde{W_{j}}\) . And the \(r\)  independent samples give us concentration around this expectation as shown in the following lemma which is a consequence of Cramér's Theorem ([1]}, pp. 30, 35).
